Abstract
We propose a quantum version of the well known minimum distance classification model called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous works. First, a quantum counterpart of the NMC for two-dimensional problems was introduced, named Quantum Nearest Mean Classifier (QNMC), together with a possible generalization to any number of dimensions. Secondly, we studied the n-dimensional problem into detail and we showed a new encoding for arbitrary n-feature vectors into density operators. In the present paper, another promising encoding is considered, suggested by recent debates on quantum machine learning. Further, we observe a significant property concerning the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a meaningful difference between the NMC and the respective quantum version, allows us to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted: (i) to compare the NMC and QNMC performance on different datasets; and (ii) to study the effects of the non-invariance under uniform rescaling for the QNMC.
Highlights
In recent years, we observed an increasing interest toward the use of quantum formalism in non-microscopic domains [1,2,3,4]
We introduce the well known Nearest Mean Classifier (NMC) [24], which is a particular kind of minimum distance classifier widely used in pattern recognition
In this work we have introduced a quantum minimum distance classifier, named Quantum
Summary
We observed an increasing interest toward the use of quantum formalism in non-microscopic domains [1,2,3,4]. The real power of quantum computing consists in exploiting the strength of particular quantum properties in order to implement algorithms which are much more efficient and faster than the respective classical counterpart. For this purpose, several non standard applications involving the quantum mechanical formalism have been proposed, in research fields such as game theory [5], economics [6], cognitive sciences [7], signal processing [8], and so on. We can find several efforts exploiting quantum information properties for the resolution of pattern recognition problems in [9], while a detailed overview concerning the application of quantum computing techniques to machine learning is presented in [10]
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